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y= 2x/(x^2+1)
y' =2( x^2 +1 -2x^2)/(x^2+1)^2
=2(1 -x^2)/(x^2+1)^2
y'=0
1-x^2 =0
x=1 or -1
y' |x=1+ <0 , y' |x=1- >0
x=1 (max)
y' |x=-1+ >0 , y' |x=-1- <0
x=1 (min)
max f(x)= f(1) =2/(1+1) =1
min f(x) = f(-1)= -2/(1+1) =-1
lim(x->+∞) 2x/(x^2+1) =0
lim(x->-∞) 2x/(x^2+1) =0
y=2x/(x^2+1)的值域 = [ -1, 1]
y' =2( x^2 +1 -2x^2)/(x^2+1)^2
=2(1 -x^2)/(x^2+1)^2
y'=0
1-x^2 =0
x=1 or -1
y' |x=1+ <0 , y' |x=1- >0
x=1 (max)
y' |x=-1+ >0 , y' |x=-1- <0
x=1 (min)
max f(x)= f(1) =2/(1+1) =1
min f(x) = f(-1)= -2/(1+1) =-1
lim(x->+∞) 2x/(x^2+1) =0
lim(x->-∞) 2x/(x^2+1) =0
y=2x/(x^2+1)的值域 = [ -1, 1]
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